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3 years ago

I need help with 35 please

Mathematics

1 answer:

Rufina [12.5K]3 years ago

6 0

Answer:

MEOWWWWWWWWWWWWWWWWWWWWWWWW

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What is the solution to this system of equations? 2t + w = 10 4t = 20 − 2w A. It has no solution. B. It has infinite solutions.

joja [24]

Answer:

<h3>B. It has infinite solutions</h3>

Step-by-step explanation:

Given the system of equations:

2t + w = 10 ..... 1

4t = 20 − 2w ... 2

From 1:

w = 10-2t ...3

Substitute 3 into 2 to have;

4t = 20 - 2(10-2t)

4t = 20-20+4t

4t = 4t

Let t = k

Substitute t = k into 1 and get w;

From 1: 2t + w = 10

2k + w =10

w = 10 - 2k

<em>k can take any integers. This shows that the solution to the equation is infinite</em>

7 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

A rectangular Corn Hole area at the Recreation Center has a width of 5 feet and a length of 10 feet. If

lbvjy [14]

Answer:

2ft

Step-by-step explanation:

5 x 10=50

7 x 12= 84

5+2=7 and 10+2=12

3 0

3 years ago

ABCD is a square. <br><br><br><br> What is the measure of angle BAC?

bezimeni [28]

Angle BAC is 45 degrees. The diagonal bisects angle BAD and since all angles in a square are 90 degrees, half of 90 is 45 degrees.

8 0

4 years ago

Read 2 more answers

A ball is thrown vertically upward with an initial velocity of 48 feet per second. The distance s (in feet) of the ball from th

ra1l [238]

Hello,

s=48t-16t²

a)
s=0==>16t(3-t)=0==>t=0 or t=3

b)
s>32==>48t-16t²>32===>16(t²-3t+2)<0
Δ=9-8=1
==>16(t-1)(t-2)<0

==>1<t<2 (negative between the roots)

5 0

3 years ago