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shusha [124]
3 years ago
6

Find the function r that satisfies the given condition. r'(t) = (e^t, sin t, sec^2 t): r(0) = (2, 2, 2) r(t) = ()

Mathematics
1 answer:
lesantik [10]3 years ago
6 0

Answer:

r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2)

Step-by-step explanation:

A primitive of e^t is e^t+c, since r(0) has 2 in its first cooridnate, then

e^0+c = 2

1+c = 2

c = 1

Thus, the first coordinate of r(t) is e^t + 1.

A primitive of sin(t) is -cos(t) + c (remember that the derivate of cos(t) is -sin(t)). SInce r(0) in its second coordinate is 2, then

-cos(0)+c = 2

-1+c = 2

c = 3

Therefore, in the second coordinate r(t) is equal to -cos(t)+3.

Now, lets see the last coordinate.

A primitive of sec²(t) is tan(t)+c (you can check this by derivating tan(t) = sin(t)/cos(t) using the divition rule and the property that cos²(t)+sin²(t) = 1 for all t). Since in its third coordinate r(0) is also 2, then we have that

2 = tan(0)+c = sin(0)/cos(0) + c = 0/1 + c = 0

Thus, c = 2

As a consecuence, the third coordinate of r(t) is tan(t) + 2.

As a result, r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2).

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A parabola intersects the X-axis at X
fiasKO [112]

Answer:

x = 6

Step-by-step explanation:

The vertex lies on the axis of symmetry which is situated midway between the x- intercepts, thus x- coordinate of vertex is

x_{vertex} = \frac{3+9}{2} = \frac{12}{2} = 6

4 0
3 years ago
A die is thrown 300 times with frequencies for the outcome 1 2 3 4 5 6, whats the probablity of getting a prime number, given th
aleksklad [387]

Answer:

58.3% to the nearest tenth.

Step-by-step explanation:

The prime numbers from 1 to 6 are 2,3 and 5.

The probability of a prime number taken from the result of the 300 throws:

=  (sum of the frequencies for 2, 3 and 5)  /  ( total throws)

= (60 + 55 + 60) / 300

=  0.5833 or 58.3%.

6 0
3 years ago
In triangle GHI the measure of angle I = 90•, HI = 5.6, and IG = 2.8 feet. Find the measure of angle G to the nearest tenth of a
Irina-Kira [14]

Answer:

63.4

Step-by-step explanation:

3 0
3 years ago
104 tests is what % of 160 tests
Afina-wow [57]
160 test=100%

Therefore:

160 test------------------100%
104 test------------------   x
x=(104 test*100%) / 160 test=65%

Answer: 104 test is the 65% of 160 test
8 0
3 years ago
Can someone please help??? WILL MARK BRAINLIEST
olya-2409 [2.1K]

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)


To find the slope, you can use the slope formula and plug in the two points:

(3,63) = (x₁ , y₁)

(5,107) = (x₂, y₂)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m=\frac{107-63}{5-3}

m=\frac{44}{2}

m = 22


Now that you know m = 22, plug it into the equation:

y = mx + b

y = 22x + b

To find "b", plug in one of the points into the equation (I will do both points)

(3,63)

y = 22x + b

63 = 22(3) + b

63 = 66 + b    Subtract 66 on both sides

-3 = b


(5,107)

y = 22x + b

107 = 22(5) + b

107 = 110 + b    Subtract 110 on both sides

-3 = b


y = 22x - 3

8 0
3 years ago
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