1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yuri [45]
3 years ago
14

Please helppp number 11

Mathematics
1 answer:
aivan3 [116]3 years ago
4 0

Answer:

(1/3)⁷

Step-by-step explanation:

negative exponents work like this:

x⁻²=(1/x)²

Apply this theory to this equation:

3⁻⁷=

(1/3)⁷

You might be interested in
Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa
Nataly_w [17]

Answer:

The first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

coefficient of x^{2} in the expansion of (2+x - x^{2})^{6} = (240 - 192) = 48

Step-by-step explanation:

(2+x)^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})

= 6_{C_{0}} \times x^{0} \times 2^{6}  + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4} + terms involving higher powers of x

= 64 + 192 \times x^{1} + 240 \times x^{2} + terms involving higher powers of x

so, the first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

Again,

(2+x - x^{2})^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})

Now, by inspection,

the term x^{2} comes from k =5 and k = 6

for k = 5, the coefficient of  x^{2}  is , (-32) \times 6 = -192

for k = 6 , the coefficient of x^{2} is, 6_{C_{2}} \times 2^{4} = 240

so,   coefficient of x^{2} in the final expression = (240 - 192) = 48

3 0
2 years ago
Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =
Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

or

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0
3 years ago
What is the length of the hypotenuse of the triangle? triangle A B C. Side A C is 7 centimeters and side B C is 3 centimeters. H
Maksim231197 [3]

Answer: √58 cm or 7.62 cm

Step-by-step explanation:

The Pythagorean Theorem is a²+b²=c². Since we are given the lengths of a and b, we can plug them into this formula to find the length of the hypotenuse.

7²+3²=c²

49+9=c²

58=c²

c=√58 or 7.62 cm

6 0
3 years ago
I need help with 2. 3. 8 and 13 please help me
Crank

Answer:

all work is shown and pictured

6 0
3 years ago
Mr. Cruz fills a 3-gallon water cooler for a family picnic. He brings plastic cups that each hold 12 fluid ounces of water. How
oksian1 [2.3K]

One gallon is equivalent to 128 fluid ounces

3 gallons is equivalent to 3*128 fluid ounces

= 384 fluid ounces

One plastic cup can hold 12 guide ounces

So cups needed will be 384/12

32 cups

8 0
2 years ago
Other questions:
  • A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain245 ounces of a mixture
    10·1 answer
  • The volume of the mold is 186 cubic feet concrete is sold by cubic yard how many cubic yards of concrete will I need to fill mol
    13·1 answer
  • Please answer and explain why.
    7·1 answer
  • What is the ordered pair of point A(2,5)after a dilation with a scale factor of 2?
    6·1 answer
  • PLEASE HELP PLEASE PLEASE PLEASE
    12·2 answers
  • A right triangle is ____ a scalene triangle.<br> Always, sometimes, or never
    11·1 answer
  • Tanner is an 8th grader in Texas and wants to attend Stanford University after he graduates from
    13·1 answer
  • Evaluate –9x - 8<br> When x = -4
    5·2 answers
  • GIVING BRAIN TO CORRECT ANSWER!!
    10·1 answer
  • Find the distance between (3,-2) and (2, -4)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!