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2 years ago

What is the solution to the system of equations?

Mathematics

2 answers:

Free_Kalibri [48]2 years ago

6 0

Answer:

negative 2, StartFraction 5 over 3 EndFraction)

Step-by-step explanation:

melamori03 [73]2 years ago

5 0

9514 1404 393

Answer:

(b) (negative 2, StartFraction 5 over 3 EndFraction)

Step-by-step explanation:

The value of x is given, so you only need to substitute that into the first equation to find y.

y = 2/3(-2) +3 = -4/3 +9/3

y = 5/3

The solution is (x, y) = (-2, 5/3).

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To the nearest hundredth of a yard, determine the circumference of the given circle. Approximate as 3.14. r=6

Bond [772]

Answer:

37.68

Step-by-step explanation:

c = 2 x 3.14 x 6

7 0

3 years ago

The diameter of a circle is 12 mm. what is its radius?

MrMuchimi

Answer:

6mm

Step-by-step explanation:

radius = 1/2 of diameter

5 0

3 years ago

Read 2 more answers

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

3 0

3 years ago

What is the answer to the multiplication problem 4×3

nika2105 [10]

Answer:

4x3=12

Step-by-step explanation:

8 0

3 years ago

How to write an equation for the line perpendiculer and trhough the given ppoint?

valentinak56 [21]

A method that always works is to find the slope of the given line, then find the negative reciprocal of that. Your result will be the slope of the perpendicular line. Using this slope and the given point, fill in the parameters of the point-slope form of the equation of a line.

For m = slope of given line and (h, k) = given point, the perpendicular line will be
y = (-1/m)(x -h) +k

Often, this equation can be simplified to another appropriate form, such as slope-intercept form (y = mx+b) or standard form (ax+by=c).

_____
The slope of a given line can be found by solving its equation for y. The slope is the coefficient of x in that solution. If the given line is characterized by two points, (x1, y1) and (x2, y2), then its slope is m = (y2-y1)/(x2-x1).

In the unusual case where the given line is vertical (x=<some constant>), the slope of the perpendicular line is zero, and the line you want becomes y=k.

5 0

3 years ago