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2 years ago

PLEASE ANSWER ASAP IT'S IMPORTANT 30 POINTS

Mathematics

2 answers:

Reptile [31]2 years ago

3 0

Answer:

√841

Step-by-step explanation:

You would use pythagorean theorem to solve this problem:

a² + b² = c²

a = 20 b = 21

20² + 21² = 400 + 441 = 841

√841

Kisachek [45]2 years ago

3 0

841 square rooted because after you square root 841 you get 29 as the hypotenuse

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A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f

NNADVOKAT [17]

Answer:

$26 - \sqrt{181}$ cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares, in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}$

$x = \frac{624 \pm \sqrt{104256}}{24}$

$x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}$

$x = \frac{624 \pm 8*3*\sqrt{181}}{24}$

$x_1 = \frac{624 + 24*\sqrt{181}}{24}$

$x_1 = 26 + \sqrt{181}$

$x_2 = \frac{624 - 24*\sqrt{181}}{24}$

$x_2 = 26 - \sqrt{181}$

But $x_1 > 33$ , then is not the correct answer.

5 0

2 years ago

How can the graph of f(x) = 1/(- x) - 9 be obtained from the graph of y = 1/x

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2 years ago

A girl threw a marble 15 m vertically up in the air which later fell and settled at the bottom of a lake 7 m deep. Find the tota

emmasim [6.3K]

Answer:

22 m

Step-by-step explanation:

Total distance travelled by marble while falling down = height above surface of lake + depth of lake = 15 + 7 = 22 m

6 0

3 years ago

The store salsa jars have a height of ten centimeters and a radius of five centimeters. If

Alex_Xolod [135]

Answer:

471.2 cm³ missing

Step-by-step explanation:

jars are cylinders

volume of cylinder = π * r² * h

h=10

r=5

v=785.4 cm³ of a full jar

r stays the same = 5

h = 4

v= 314.2 cm³ left in the jar

whats missing is the full-left

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6 0

3 years ago

Jace is a songwriter who collects royalties in his songs whenever they are played in a commercial or a movie. Jace will earn $50

VashaNatasha [74]

Jace's song were played on 8 commercials and 2 movies

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

<em>Number of Commercials = C</em>

<em>Number of Movies = M</em>

$\texttt{ }$

<em>Jaces songs were played on 6 more commercials than movies.</em>

$\boxed{C = 6 + M}$ → <em>Equation 1</em>

$\texttt{ }$

<em>Jace will earn $50 every time one of his songs is played in a commercial and he will earn $140 every time one of his songs is played in a movie.</em>

<em>His total earnings in the royalties from all commercials and movies was $680.</em>

$\boxed{50C + 140M = 680}$ → <em>Equation 2</em>